Voltage Regulator (need a quick question answered)

[BP-Revo]

Ok, I have a Hitec CRX Transmitter. It currently uses a 8 cell AA rechargeable pack for power. There are also optional trays that allow to use of 8 AA (non-rechargeable). An alkaline is 1.5V fully charged, so I assume the radio can take as high as 12V.

I bought a 3S lipo pack for it, but as we all know, that charges to 12.6V. I dont want to fry my radio, so I plan to pick up a simple voltage regulator to bring the voltage down to 11V (if I can find one, I know they have 10V ones available). My controller has a built in voltage detector and starts beeping if voltage falls below 9V.

So, I figure that voltage will just hold 10/11V constant with the regulator, and once the battery voltage falls below that, then output voltage will just equal battery voltage, correct?

Basically, in short, when the input voltage to a voltage regulator is less than what the regulator brings the voltage to, it just equals input voltage? (ie, given a 12V voltage regulator, if input is 11v, so is output).